Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.
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Tuesday, July 5, 2016
Geometry Problem 1231: Triangle, Orthocenter, Incenter, Circumcenter, Angle Bisector, Center, Circle
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https://goo.gl/photos/eZPPUPkAJ3njjb2E7
ReplyDeleteDraw OD ⊥ to AC ( D is on the circle O)
D is the midpoint of arc AC
since BI is the angle bisector of ∠(ABC) => B, I, D are collinear
Triangle BOD is isoceles => ∠(OBI)=∠(ODI)
but ∠(ODI)=∠(HBI) => ∠(HBI)=∠(OBI) => BI is the angle bisector of ∠( HBO)
see correct link to this problem below:
Deletehttps://goo.gl/photos/NtEqqUcJsf3GfQgm6
Peter Tran
Prøblem 1231
ReplyDelete< ABI = < CBI ......(1)
< ABH = < CBO = 90-A ....(2)
(1) - (2) gives the required result
Sumith Peiris
Moratuwa
Sri Lanka